Types of materials (metal

Types of materials (metal

1. Band Picture — Metal (Conductor)

Metal: valence band overlaps conduction band, or Fermi level inside a band, so no gap to cross — electrons already free to move under tiny $E$.

• Band diagram:

inside allowed band ⇒ partially filled band ⇒ many states at $E_F$ for conduction.

• Resistivity: very low $∼10^{-8}$ Ω·m (Cu), decreases slightly with $T$? Actually increases with $T$ due to phonon scattering ($ρ∝T$), opposite to semiconductor.
• Carrier concentration: $n∼10^{28}$ m⁻³ (every atom contributes ~1 e⁻).

Examples: Cu, Al, Ag, Fe. Used for wiring, interconnects.

2. Why Metal Conducts Even at 0 K

Fermi sea filled to $E_F$; infinitesimal energy excites electrons at $E_F$ to just above, no gap. So metal always conducting.

3. Exam Distinction (with next topics)

Next topics will cover semiconductor (small gap $∼1$ eV, thermally excitable) and insulator (large gap $>3$ eV, not excitable at room $T$).

4. Exam Points

• Draw band diagram for metal (overlapped bands, $E_F$ in band) — 5 marks, very frequent (part of 3-type comparison).
• State $ρ∼10^{-8}$ Ω·m and $ρ$ increases with $T$ — 3 marks.
• Give examples — 3 marks.